MANAGING THE USE OF APPROXIMATION MODELS IN NONLINEAR PROGRAMMING

Michael Lewis, Institute for Computer Applications in Science and Engineering; Natalia Alexandrov, NASA Langley Research Center; Virginia Torczon, College of William and Mary and Institute for Computer Applications in Science and Engineering; John Dennis, Rice University

The research effort in optimization described here is one of several CRPC projects being conducted by scientists at the Institute for Computer Applications in Science and Engineering (ICASE), a CRPC affiliate site since 1995. Michael Lewis of ICASE, Natalia Alexandrov of NASA Langley Research Center (LaRC), and Virginia Torczon of the College of William and Mary and ICASE, in collaboration with Rice University Optimization Project Director John Dennis, are investigating ways to make optimization practical and useful for engineering applications. The current focus of their work is managing approximation models for engineering optimization and design.

Frequently, engineers cannot make use of the latest developments in numerical optimization techniques. This difficulty is primarily due to limited exchange of information between engineers and numerical analysts. In particular, nonlinear programmers may not understand what is necessary to convert their analytical and algorithmic developments into accessible tools of interest to engineering practitioners. Managing the use of approximation methods in nonlinear programming is one step toward addressing this gap.

Considerable effort in many engineering and scientific fields has been devoted to the development of computational models of high fidelity to capture complex physical phenomena. This is the case, for instance, in computational fluid dynamics and structural engineering. However, the computational expense of such simulations often makes them impractical for use in design optimization applications, even when run in a parallel computing environment. It is usually necessary to run these simulations repeatedly in the process of exploring the design space for improved designs. At the same time, there are generally available models of lower physical fidelity but manageable computational cost. One would like to make use of such approximation models in the iterative process of design and optimization.

The ICASE/LaRC research group is developing techniques to use approximation models in a systematic way in the setting of optimization. The obvious issue that must be addressed is that a lower-fidelity model may fail to predict accurately the behavior described by the high- fidelity model of the system being optimized. There is no guarantee that a design that promises improvement when an approximation is used will yield improvement for the system described by the high-fidelity model. Indeed, it is not unusual to observe significant differences between the behavior predicted by an approximation model and the behavior predicted by a detailed simulation.

To address this problem, the ICASE/LaRC researchers have devised a model management strategy that monitors the ability of the approximation models to predict the behavior of the system being optimized, and thereby control the amount of optimization done with the approximation models before checking the validity of the resulting design via a high- fidelity simulation. The work at ICASE/LaRC focuses on developing model management strategies that use sensitivity information in conjunction with quasi-Newton methods for nonlinear programming. The use of approximation methods will make optimization software such as that developed by the CRPC more useful for engineering applications. The LaRC application currently targeted for testing is a wing-box model of a high-speed civil transport.

For more information about this project, see http://www.icase.edu/ .

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